Livermore has excelled for the Tigers during a season-long loan from Tottenham and Bruce has made no secret of his desire to make the arrangement a long-term one.
Managerial uncertainty at White Hart Lane, where Tim Sherwood appears to have a tenuous grasp on the top job, muddies the waters somewhat but Bruce is confident a deal can be done as long as he has the necessary funds.
And, with a step increase of over £1million for every place in the table, Hull's final league standing could play its part.
Bruce said: "The prize money at stake is probably the difference between me getting another player.
"We've budgeted to be 20th, so anything on top of that might help me bag Jake Livermore, for example.
"It's important that we stay where we are. We've been around the 13th or 14th mark since last September, so my aim is to stay there until at the end of the season.
"The first piece of business I'll try to do is to secure Jake if I can. I'll do everything I can to buy him."
Bruce has also had positive signals from the player, who was forced down the pecking order at Spurs under previous boss Andre Villas-Boas.
"I think everyone knows my stance and, all things being equal, Jake would like to stay here," he said.
"I would love to do something quickly, if we possibly can. Jake has indicated to us that he would like to stay, so we'll see how it develops."
Bruce's own deal at the KC Stadium is a 12-month rolling contract, though reports have emerged that the club's impressive return to the top flight, as well as their run to the FA Cup final, might earn him a longer-term offer.
He will meet owner Assem Allam in the next two weeks for talks but is in no hurry to force the issue.
"I've had a great couple years here. If I'd have had said we'd go from a Championship team to getting promoted, staying up, reaching an FA Cup final and getting into Europe, I think they'd have been coming for me in white coats and vans to take me away," he said.
"I've got a contract which goes into a 12-month rolling contract in June. It's up to the people who employ me. I'm very happy here, why shouldn't I be?
"If they want to secure it longer than that, it's up to them. It's their call. Everybody likes a pay rise.
"But supporters need not worry. I'm very happy. They've been great towards me and long may that continue."
- Sports & Recreation
- Jake Livermore
- Tim Sherwood